In boundary changes agreed in 2006, Greenway's constituency was enlarged and renamed Thirsk and Malton, taking in a large part of the divided Vale of York constituency. Unexpectedly on 18 November 2006, the Thirsk and Malton Conservative Association selected Anne McIntosh (sitting MP for Vale of York) over Greenway as their candidate for the next general election.

He has been criticised in some quarters for his poor attendance record in the House of Commons. According to the theyworkforyou website, he has attended only half of Parliamentary votes, and has contributed to very few debates. In the ongoing scandal concerning MP's expenses it is alleged Mr. Greenway claimed £500 for petunias and fuchsia for his London flat. [1]

He was married to Sylvia Ann Gant in 1974. They have two sons and a daughter. He now lives in Chiswick with divorcee Hanneke Dannhorn (born 1953), mother of Emily and Mark Dannhorn, and managing director of the Brook Green UK travel group, since 2004.

A horse racing enthusiast, he won an animal welfare award in 2003, and is the president of York City F.C. As a former police officer he has called for the death penalty for police murders, specifically mentioning Winston Silcott, after narrowly avoiding being shot. Greenway fought for an amendment to the Criminal Justice Act 1991 to provide for capital punishment for the murder of a police officer. He later tried to sponsor a similar bill commanding that "A person aged 18 years or above who is convicted of the murder of a police officer acting in the execution of his duty shall on conviction be sentenced to death." Both attempts were soundly defeated.[2]